I think there's a basic design problem if nothing else.

A photo from above shows the floor of the roof paneling extending almost completely past the downspout ( it's worse than the pic shows) which would have the water banging off the front with the resultant splashing over.

I did put some drain cleaner in the pipe-it worked very well in the shower drain so...

I think I'll affix a block off plate over the rectangular opening in the second photo which will stop the splashing over.